In this case-study, we examine the effects of linear control on continuous dynamical systems that
exhibit chaotic behavior using the symbolic computer algebra system Mathematica. Stabilizing (or
controlling) higher-dimensional chaotic dynamical systems is generally a difficult problem, Musielak
and Musielak, [1]. We numerically illustrate that sometimes elementary approaches can
yield the desired numerical results with two different continuous higher order dynamical systems
that exhibit chaotic behavior, the Lorenz equations and the R？ssler attractor.
References
[1]
Musielak, Z.E. and Musielak, D.E. (2009) High-Dimensional Chaos in Dissipative and Driven Dynamical Systems. International Journal of Bifurcation and Chaos, 19, 2823-2869.
[2]
Chun, F.Y., Wang, H., Hu, Y. and Yin, J.W. (2012) Antisynchronization of a Novel Hyperchaotic System with Parameter Mismatch and External Disturbances. Pramana-Journal of Physics, 79, 81-93.
[3]
Li, Y. and Li, B. (2009) Chaos Control and Projective Synchronization of a Chaotic Chen-Lee System. Chinese Journal of Physics, 47, 261-279.
[4]
Tan, X., Zhang, J. and Yang, Y. (2003) Synchronizing Chaotic Systems Using Backstepping Design. Chaos, Solitons, Fractals, 16, 37-45.
[5]
Vieira, D. and Lichtenberg, A.J. (1966) Controlling Chaos Using Nonlinear Feedback with Delay. Physical Review E, 54, 1200-1207.
[6]
Wang, X.Y. and Wu, X.J. (2006) Tracking Control and Synchronization of Four-Dimensional Hyperchaotic Rössler System. Chaos, 16, 03312. http://dx.doi.org/10.1063/1.2213677
